Problem: Rewrite as a simplified fraction. ${2.21\overline{2} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2212.2222...\\ 100x &= 221.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1991}$ ${x = \dfrac{1991}{900}} \text{or} {2 \dfrac{191}{900}}$